Problem: Find the larger of the two distinct solutions to the equation $$x^2 - 11x - 42 = 0.$$
Solution: Factoring, we find that $x^2 - 11x - 42 = (x - 14)(x + 3) = 0.$ Therefore, our solutions are $-3$ and $14,$ and the larger of those two values is $\boxed{14}.$